This paper investigates nonlinear free vibration of three-dimensional graphene foam skeleton reinforced rectangular plates. The three-dimensional graphene foam skeleton can distribute in different patterns along the thickness direction of the plate. According to the mixing rule, the effective Poisson’s ratio, mass density and elastic modulus of three-dimensional graphene foam reinforced (3D-GFR) plates are described. In the framework of the von Kármán nonlinear plate theory, Hamilton’s principle is utilized to derive equations of motion. Then, analytical nonlinear frequencies of 3D-GFR plates are solved by using the Galerkin method and the harmonic balance method. Results show that 3D-GFR plates exhibit hardening nonlinearity. The effect of porosity coefficient on nonlinear vibration depends on the foam skeleton distribution. In addition, the nonlinear frequencies of 3D-GFR plates increase as the skeleton weight fraction rises.

本文研究了三维石墨烯泡沫骨架增强矩形板的非线性自由振动。三维石墨烯泡沫骨架可以沿板的厚度方向以不同的图案分布。根据混合规则，描述了三维石墨烯泡沫增强（3D-GFR）板的有效泊松比，质量密度和弹性模量。在vonKármán非线性板理论的框架中，利用汉密尔顿原理导出运动方程。然后，利用Galerkin法和谐波平衡法求解3D-GFR板的解析非线性频率。结果表明3D-GFR板表现出硬化非线性。孔隙率系数对非线性振动的影响取决于泡沫骨架的分布。此外，